The C-class AMG has high beam lights in the front bumper; not fog lights. The headlights on the C-class AMG are exactly the same as on other C-classes and the additional lights in the bumper are high beamers.

The pre "98 models of the C-classes had a ventilation opening in the front bumpers and a ventilation duct towards the (ventilation opened) mud covers in front of the front wheels. Since the C-class model update mercedes left out these ventilation ducts to the front brakes. The ventilation ducts are left out and the mud covers underneath the front fenders do not have a ventilation opening any more.

The ventilation opening in the front bumpers of the older C-classes are not the right size to easily put in some AMG beamers. The original MB bumper lights (of any possible MB model) do not fit the original C-class bumpers and it is quiet hard to fit in some descend looking beamers yourself.
The model "98 C-class came with two different front bumpers (one type for the "classic" and "elegance" and a slightly different version for the "esprit" and "sport". The ventilation holes in these bumpers are still present, but not in use to ventilate the front brakes. The shape of these ventilation holes are different as the ones in the older models, but I haven't seen easy to fit beamers for these bumpers either.

So to answer your questions: NO, Not Applicable, NO, NO and wiring WITH relay is preferred...

blackmercedes,

The older C-classes had the high beam lights underneath the normal, main lights and the fog lights besides the grill (as with the W201 and W124), the modified "98 and newer C-class have the foglights below the main lights and the high beamers besides the grill.
I thought that your car was pre "98, but the light units with the foglights below the main lights were introduced with the model change 09-"97...